We have been talking in our Developing Number Sense series about how math can become hard for children (and adults!) when they have not developed good sense about numbers early on.

Today, I want to talk about the four key number relationships children need to learn to become proficient with addition and subtraction. Children should be exposed to these number relationships after they have developed these Five Early Math Skills.

If you want an overview of number sense first, you can click here.

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**Number Relationship 1: Subitizing**

Subitizing is the ability to ‘know’ how many objects there are without having to actually count the number of objects. Most people can do this with objects up to five unless the objects are arranged in a pattern they have learned. If they are arranged in a learned pattern, such as dice, then we are able to subitize larger quantities. You can learn more in:

**Visualizing Numbers: A Key Skill to Learning Math**

For games to practice subitizing, download these FREE Subitizing Cards and then check out the list of Subitizing Games:

**Number Relationship 2: One and Two More or Less**

Learning one and two more and less than a given number gets children started on learning their basic math facts. It also allows children to become flexible thinkers and have a variety of strategies for solving problems. For example, if a child needs to add 39 + 5 and they understand that 39 is one less than 40, then they know that the answer is one less than 40 + 5. This is a much easier problem to solve in one’s head.

#### Skills You Need First

Some skills to practice before working on this relationship include counting to 100 by 1s and 2s with even and odd numbers. Once these methods of counting are fluid, then practice counting backwards these three different ways. Then, children will quickly catch onto this relationship once they are taught it.

You can also practice these skills using a number routine such as I Say, You Say.

#### How To Teach This Relationship

To teach the relationship, start by adding 1 to numbers. Children can do this by adding beads on an abacus, adding tiles or other manipulatives to a row or by moving their finger along a number path. For example, place four tiles in a row and then have them add one more and say 4 + 1 = 5. Then, add one more and say 5 + 1 = 6, and so on. Once they get the hang of this, give them a variety of ___ + 1 = problems to solve using the manipulatives if they need them.

Next, you can use this strategy and the idea of even and odd numbers to teach children to add two to a number.

Lastly, use these same techniques for teaching children to take away one and two. This is where practice counting backwards will come in handy. Then, have them use manipulatives and as they show understanding, give them a variety of ___ – 1 = and ___ – 2 = problems to solve.

**Number Relationship 3: Make Friendly 5 and 10**

Learning the numbers that add to 5 (e.g., 1 + 4, 2 + 3) and 10 (e.g., 3 + 7, 2 + 8) is another great step in children learning their addition (and later subtraction) facts. It also allows children to become flexible thinkers and solve problems in a variety of ways since we use a base 10 system. If a child knows 3 + 7 = 10, it makes a problem like 53 + 7 easier to solve.

An abacus and 5 and 10 frames are good manipulatives for teaching these combinations. (You can download 5 and 10 frames in the FREE Number Sense Packet in Developing Number Sense.)

Enter a number of beads on the first row of the abacus and see how many are left on that row that have not been entered. Or pick a 5 frame or 10 frame card and see how many boxes are filled in and how many are not. Adding those two numbers together will equal 5 or 10. If you use a blank 5 or 10 frame, than the child can place manipulatives over some of the boxes and create their own equations that add up to 5 and 10.

**Number Relationship 4: Understanding Part-Part-Whole**

Breaking numbers apart or decomposing is an important skill that will be used at all levels. Part-Part-Whole Circles are a great way for children to visualize how the numbers all relate to each other. You can learn more at:

**Build Number Sense with Part-Part-Whole Circles**

Once your children have started to gain a good understanding of these four number relationships, then you can move on to teaching all of the addition facts:

**What Order Should We Teach Addition Facts In?**